Polyomino convolutions and tiling problems

Abstract

We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases that are not detectable by generalized coloring arguments.

8 pages, 8 figures. To appear in \emph{J. of Combin. Theory Ser. A}